// test_factorial.cpp   the simplest example of a recursive function
//                      a recursive function is a function that calls itself

static int factorial(int n)  // n! is n factorial = 1*2*3*...*(n-1)*n
{
  if( n <= 1 ) return 1;     // must have a way to stop recursion
  return n * factorial(n-1); // factorial calls factorial with n-1
}                            // n * (n-1) * (n-2) * ... * (1)

#include <iostream>
using namespace std;

int main()
{
  cout << " 0!=" << factorial(0)  << endl; // Yes, 0! is one
  cout << " 1!=" << factorial(1)  << endl;
  cout << " 2!=" << factorial(2)  << endl;
  cout << " 3!=" << factorial(3)  << endl;
  cout << " 4!=" << factorial(4)  << endl;
  cout << " 5!=" << factorial(5)  << endl;
  cout << " 6!=" << factorial(6)  << endl;
  cout << " 7!=" << factorial(7)  << endl;
  cout << " 8!=" << factorial(8)  << endl;
  cout << " 9!=" << factorial(9)  << endl;
  cout << "10!=" << factorial(10) << endl;
  cout << "11!=" << factorial(11) << endl;
  cout << "12!=" << factorial(12) << endl;
  cout << "13!=" << factorial(13) << endl;
  cout << "14!=" << factorial(14) << endl;
  cout << "15!=" << factorial(15) << endl; // expect a problem with
  cout << "16!=" << factorial(16) << endl; // integer overflow
  cout << "17!=" << factorial(17) << endl; // uncaught in C++  (Bad!)
  cout << "18!=" << factorial(18) << endl;

  return 0;
}

// output of execution is:
//  0!=1
//  1!=1
//  2!=2
//  3!=6
//  4!=24
//  5!=120
//  6!=720
//  7!=5040
//  8!=40320
//  9!=362880
// 10!=3628800
// 11!=39916800
// 12!=479001600
// 13!=1932053504  // wrong! 13! = 12! * 13, must end in two zeros
// 14!=1278945280  // wrong! and no indication!
// 15!=2004310016  // wrong!
// 16!=2004189184  // wrong!
// 17!=-288522240  // wrong and obvious if you check your results
// 18!=-898433024  // Only sometimes does integer overflow go negative